Sulfur can violate the octet rule because it has an "empty D orbital" is there any other information the periodic table isnt telling us?

Question

In sulfur or any atom with an expanded octet on the 3rd row, where does the idea that they have an empty D orbital come from ?

Answer 1

Sulphur does not expand its octet. That was a hypothesis proposed long ago and vehemently supported by Linus Pauling. While Linus Pauling had a few very great ideas that moved chemistry forward, he also made some major blunders like the octet expansion hypothesis or seven grams of vitamin C a day. Possibly because of Pauling’s status and Nobel Prize, octet expansion remains to be present in high school textbooks to this day and even professors still believe in it.

Back in the day, a competing hypothesis to explain compounds such as $\ce{SO3}$ was proposed: charge separation. In a nutshell, the central sulphur atom does not take part in three double bonds (which would expand the octet) but rather forms two $\ce{\overset{+}{S}-\overset{-}{O}}$-type single bonds and one regular double bond for a total of eight electrons. On paper, these bonds can switch back and forth so that each oxygen gets one third of the double bond share (in reality, they do not switch; every bond has the bond order 1.333, all are equal length and so on. This is resonance, akin to what is found in benzene, and often called Y-aromaticity on this site). You can learn more about $\ce{SO3}$ in this wonderfully detailed answer.

In the case of $\ce{SF6}$, fluorine can only form single bonds to sulphur. So instead of a $\ce{\overset{+}{S}-\overset{-}{O}}$ bond we see a $\ce{\overset{+}{S}\bond{...}\overset{-}{F}}$ bond which is always opposite a ‘normal’ $\ce{S-F}$ bond, so together they form a $\ce{F-\overset{+}{S}\bond{...}\overset{-}{F}}$ 4-electron-3-centre bond with a similar resonance phenomenon; this type of bond probably won’t get introduced for a while in your curriculum.

Now what about this ‘empty d orbital’? Well, that actually ‘exists’ and can be derived from quantum mechanics. You may have heard of the $2n^2$ rule for predicting how many electrons can fit into a shell—but at the same time heard of the octet rule which means that after Ar the next electron gets added into the 4th shell although there is still space for ten more electrons in the 3rd shell. Well, quantum mechanics tells us that shells can be divided into subshells; we call these s, p, d, f, g, h, …. Quantum mechanics also tells us that the $n^\text{th}$ shell has exactly $n$ subshells in the order I have given them there (so 1st shell has only s, 2nd has s and p, 3rd has s, p, d; and so on). As sulphur’s position in the periodic table tells us that its valence shell is the 3rd shell, it follows that its 3d subshell of the third shell ‘exists’.

The term to exist is stretched a little here. Technically, these orbitals don’t exist at all, they are only ‘paths’ the electrons can ‘follow’ (also two wrong terms but they get the picture across). Only if an electron is excited to a higher energy level will a higher-level (sub)shell be observable. So without electrons, do the shells exist—does a falling tree make a sound if nobody hears it? On the other hand, the energy levels are there. They can be calculated, we can hurl energy at electrons and they can then get excited to these shells. Thus, in molecular calculations these unoccupied shells are usually called virtual: there, but not quite.

So in a lengthy discussion I have established that these empty d orbitals exist. Why can’t they be used in bonding? Well, the most obvious point is hidden in the aufbau principle. Basically, it is the more elaborate octet prediction and says that after putting all possible electrons into 3p the next electron must go into 4s because 4s has a lower energy level in the ground state than 3d. This shows the rather large energy gap between p and d orbitals of the same shell which is one reason why they do not participate in bonding to any meaningful extent.

Answer 2

The discussion surrounding SF6 is often centered around two opposing hypotheses:

(1) Hypothesis # 1: SF6 actually obeys the octet rule, because the sulfur atom has a net positive charge and some of the S-F bonds are ionic in nature. For example, four single S-F bonds and two ionic S - F bonds. The six equal S-F bond lengths are then explained as a resonance among all possible placements of the ionic and covalent bonds.

(2) Hypothesis # 2: SF6 has twelve shared valence electrons which form six polar-covalent bonds. In other words, there are six single-order S-F bonds in SF6, and this sulfur atom does not obey the octet rule. In this case, some of the sulfur valence electron(s) are promoted to the 3d subshell.

Without quantitative calculations it would be impossible to determine whether hypothesis # 1 or # 2 is the correct one. The main requirements for determining whether hypothesis # 1 or # 2 is the correct one are: (i) a rigorously correct method to quantify spdfg populations of atoms in materials is required to correctly quantify the (non-tail) d-electron population of S in SF6 and (ii) a rigorously correct method to quantify bond orders is required to determine whether the sum of S-F bond orders is approximately four (as in hypothesis # 1) or approximately six (as in hypothesis # 2). Only recently have rigorous methods been developed to do this. The following journal article shows the sum of S-F bond orders in SF6 is approximately six, which supports hypothesis # 2:

T. A. Manz, “Introducing DDEC6 atomic population analysis: part 3. Comprehensive method to compute bond orders,” RSC Advances, 7 (2017) 45552-45581 (open access) http://doi.org/10.1039/c7ra07400j